There's no general address requirement shared by all, or even most, branches of government.

OSAP just cares where you're living when you're in school, but only if you're actually on OSAP. If you're no longer on OSAP, all they care about is having a place to send a collection notice if you stop paying, which is why it's easier to move mountains than it is to convince them 15 years later when you're living half way across the country that you're no longer a child and your parent's address is no longer your permanent address. (I bet you'll never guess how I know.)

MTO might care where you're living, but I'm not sure how much. Provinces only really care that you switch your DL to another province as fast as possible if you move to another province, and health insurance within 90 days.

But there is absolutely no rule that you would have to keep your DL at your parent's address. That is just nutty and you'd do well never to take advice from anyone who claims that.

Revenue Canada only cares what province you lived in at the end of the tax year.

Not sure if there are any other organizations that would care.

Hope that helps!